OBJECTIVE: THE STUDENT WILL EXPLORE THE VOLUME OF A FUNCTION ROTATED AROUND THE X-AXIS BY USING 1/2 A NERF FOOTBALL.
USING THE FORMULA FOR A CYLINDER, USING THE FUNCTION AS THE RADIUS, THE STUDENT WILL FIND THE VOLUME OF THE SOLID FORMED BY ROTATING THE FUNCTION AROUND THE X AXIS.
 

BENCHMARKS

N-5-H, P-1-H, P-5-H, D-1-H, G-3-H, A-1-H, A-3-H

TIME  FRAME

2-3 CLASS PERIODS

CURRICULUM INTEGRATION

GEOMETRIC FIGURES, FUNCTIONS, VOLUMES OF SUBSTANCES, WATER TANKS, PARABOLIC REFLECTORS, FORMULAS

MATERIALS

EACH GROUP OF 4 WILL HAVE 2 EACH 1/2 NERF FOOTBALL (CUT TO FORM 2 PARABOLIC SOLIDS), A HACKSAW, A RULER, AND 2 DOWEL RODS FORMED INTO COORDINATE AXES.

APPLICATIONS

MANUFACTURING AND FIGURE ANALYSIS,  CONSTRUCTION,

STUDENT GROUPINGS

4 OR 5 STUDENTS

EVALUATION: 

THE STUDENT WILL BE EVALUATED ON HIS/HER CONTRIBUTION TO THE EFFORT OF THE GROUP  BY THE TEACHER AND GROUP MEMBERS, BY EVALUATION FORM.
 

PROCEDURES:

THE STUDENTS WILL BE GIVEN AS MUCH TIMES AS NEEDED TO TAKE ONE OF THE HALF-FOOTBALL AND, USING ANY METHOD THEY CHOOSE, TRY TO DETERMINE THE VOLUME OF THAT SOLID.

AFTER THEY HAVE EXHAUSTED ALL POSSIBILITIES, THE STUDENTS WILL CUT THE OTHER HALF LENGTH-WAYS AND MOUNT ONE HALF ON THE COORDINATE AXES, TAKE MEASUREMENTS FOR X AND Y, ENTER THESE INTO THE TABLES OF A GRAPHING CALCULATOR, AND WRITE THE EQUATION OF THE FUNCTION (THE OUTLINE OF THE POSITIVE SIDE OF THE SKIN OF THE FOOTBALL.
 
 

EXTENSION:

THIS LESSON LEADS TO FINDING VOLUMES BY INTEGRATION.